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Reading Serre's letter to Gray , I wonder if now modern expositions of the themes in Klein's book exist. Do you know any?

edited Dec 21 2009 at 15:16

Ben Webster♦
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asked Dec 21 2009 at 14:37

Thomas Riepe
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The link should go to page 550 of the book, presumably. – Mariano Suárez-Alvarez Dec 21 2009 at 14:42

Jerry Shurman · Accepted Answer · 2010-01-23 06:08:31Z UTC

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"Geometry of the Quintic" is available for free at my website.

Jerry Shurman

answered Jan 23 2010 at 6:08

Jerry Shurman
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Wonderfull! Thanks! – Thomas Riepe Jan 23 2010 at 8:56

Kristal Cantwell · Answer 2 · 2009-12-21 17:59:45Z UTC

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In Glimpses of algebra and geometry by Gabor Toth, chapter 25 is devoted to Klein's main result.

answered Dec 21 2009 at 17:59

Kristal Cantwell
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Oliver Nash · Answer 3 · 2012-02-05 19:55:51Z UTC

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I got interested in this subject last year and just got round to writing up some notes which I hope may be of use.

I also have a python script which implements the Klein's icosahedral solution of the quintic linked from this page.

answered Feb 5 2012 at 19:55

Oliver Nash
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Great! Thanks! – Thomas Riepe Feb 5 2012 at 21:31

Alon Amit · Answer 4 · 2009-12-21 15:25:29Z UTC

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Chapter 5 of McKean and Moll's "Elliptic Curves" explores the circle of ideas around Ikosaeder.I'm not sure if you'd consider this sufficiently "modern" - it's certainly a contemporary book but it doesn't use, say, scheme-theoretic language.

answered Dec 21 2009 at 15:25

Alon Amit
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It looks like our identical answers crossed paths! You beat me by one minute, so I'll delete my answer. – Andy Putman Dec 21 2009 at 19:18

lol, you're right - I caught it just before you deleted. Very gallant of you! and hey, in math, every minute counts. :-) – Alon Amit Dec 21 2009 at 19:58

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As an aside to everyone else -- McKean and Moll's book is really beautiful! I read large chunks of it as an undergraduate, and I still go back to it periodically. – Andy Putman Dec 21 2009 at 20:12

David Lehavi · Answer 5 · 2009-12-21 22:00:46Z UTC

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There is the outrageously expansive "Geometry of the quintic" by Jerry Shurman, which discusses both Klein and Doyle-McMullen approaches (and then some more).

answered Dec 21 2009 at 22:00

David Lehavi
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	"expensive", yes. – lhf Dec 21 2009 at 22:51
	since it's softcover with horrible print quality - yes it is. – David Lehavi Dec 22 2009 at 5:07
	See Jerry Shurman's answer for a link to a free copy ;) – Dr Shello Jan 12 2011 at 8:33
	Re: Dr. Shello - yes, Shurman remarked a few months ago on MO he made the text publicly available. This answer predates his release. – David Lehavi Jan 12 2011 at 9:03

Do there exist modern expositions of Klein’s Icosahedron?

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